A new cavitation model in lubrication: the case of two-zone cavitation

A generalization of the Elrod–Adams model of cavitation in lubricated devices is proposed, such that the translation velocity $V$ for the saturation field $\mathit{\theta }$ can be given any value between $S/2$ and $S$ , with $S$ being the relative speed of the surfaces. The lack of uniqueness of the classical model when $V\ne S/2$ is explained and a suitable supplementary condition is proposed to fix this issue. The new model is rigorously analyzed, though in the simplified mathematical setting of a one‐dimensional problem with a single pressurized region. The main result states the existence of a unique solution globally in time, unless of course the cavitation boundary leaves the domain or disappears. A few preliminary numerical examples are included to illustrate the model.